Finite Group Databasebeta

C23×#14273637 #29452071

order15104
automorphism?
homologyAbelianization (H1) = C23×C42 · Schur multiplier (H2) = C210

Aliases

direct productC23×#14273637

Splittings

SylowC59 ⋊ C23×#97

Subgroups

subgroupG/H
centerC24×C4C2×D59
commutatorC2×C59C23×C42
FrattiniC2×C4C24×D59
FittingC24×C8×C59C2
socle, prime radicalC25×C59C2×C4
cosocleC2×C4×C59C25
hypercenterC24×C8D59
hypocenterC59C23×#97
LCSG ▷ C2×C59 ▷ C59
UCSC1 ◁ C24×C4 ◁ C24×C8

4126 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15104

Conjugacy classes & character table

3872 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 1032950);